linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular...

vectors and their coordinate vectors maps vector addition to vector addition and scalar multiplication to scalar multiplication. It is thus a vector space...

In mathematics, a set B of vectors in a vector space V is called a basis (pl.: bases) if every element of V may be written in a unique way as a finite...

particularly important for understanding how the coordinate description of a vector changes by passing from one coordinate system to another. Tensors are objects...

physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude...

ordered basis of a vector space of finite dimension n allows representing uniquely any element of the vector space by a coordinate vector, which is a sequence...

numbers, also known as coordinate vectors. Special cases are called the real line R1, the real coordinate plane R2, and the real coordinate three-dimensional...

of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is called a coordinate vector...

Cartesian coordinate system. For instance, the standard unit vectors in the direction of the x, y, and z axes of a three dimensional Cartesian coordinate system...

measures the same vector with respect to a different background coordinate system. The transformation properties of vectors distinguish a vector as a geometrically...

the vector on the basis. These coordinate vectors form another vector space, which is isomorphic to the original vector space. A coordinate vector is commonly...

The coordinates of the vector r with respect to the basis vectors ei are xi. The vector of coordinates forms the coordinate vector or n-tuple (x1, x2, …...

(usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely...

x-y coordinate system, the above formula for gradient fails to transform like a vector (gradient becomes dependent on choice of basis for coordinate system)...

Vector notation In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more...

are given as in finite coordinate space. The dimensionality of F∞ is countably infinite. A standard basis consists of the vectors ei which contain a 1 in...

description of the plane was later generalized into the concept of vector spaces. Many other coordinate systems have been developed since Descartes, such as the...

Laplacian) can be transformed from one coordinate system to another, according to transformation rules for scalars, vectors, and tensors. Such expressions then...

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified...

In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property...

a rectangular array, the coordinate vector of x ⊗ y {\displaystyle x\otimes y} is the outer product of the coordinate vectors of x {\displaystyle x} and...

{k} } where f(t), g(t) and h(t) are the coordinate functions of the parameter t, and the domain of this vector-valued function is the intersection of the...

"rotation" in a plane spanned by a space unit vector and a time unit vector, while formally still a rotation in coordinate space, is a Lorentz boost in physical...

In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional...

In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an object with four components, which transform in a specific way under...

of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the...

derivative q ˙ {\displaystyle \mathbf {\dot {q}} } of the generalized coordinate vector q of a system and the kinetic energy T of that system, by the equation...

basis) of a coordinate vector space (such as R n {\displaystyle \mathbb {R} ^{n}} or C n {\displaystyle \mathbb {C} ^{n}} ) is the set of vectors, each of...

bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields X...

and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position ( r {\displaystyle \mathbf {r}...